Search NASA⌕ Search

SEARCH · Search NASA

Results for “Nonlinear model identification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

An implementable digital adaptive flight controller designed using stabilized single-stage algorithms

An explicit adaptive controller, which makes direct use of on-line parameter identification, has been developed and applied to both the linearized and nonlinear equations of motion for the F-8 aircraft. This controller is composed of an on-line weighted least squares parameter identifier, a Kalman state filter, and a real model following control law designed using single-stage performance indices. The corresponding control gains are readily adjustable in accordance with parameter changes to ensure asymptotic stability if the conditions of perfect model following are satisfied, and stability in the sense of boundedness otherwise. Simulation experiments with realistic measurement noise indicate that the controller was effective in compensating for parameter variations and capable of rapid recovery from a set of erroneous initial parameter estimates which defined a set of destabilizing gains.

Alag, G.↗

Vibration control experiment design for the 15-m hoop/column antenna

A test program is designed for a ground-based vibration control experiment utilizing as the test article the 15-M Hoop/Column Antenna. Overall objectives of the designed ground-based test program include: (1) the validation of large space structure (LSS) control systemm techniques; (2) the validation of LSS parameter identification techniques: (3) the evaluation of actuator of actuator and sensor placement methodology; and (3) the validation of LSS computer models. Critical concerns in LSS Controls and Dynamics are: low frequency vibrational modes, close modal spacing, parameter uncertainties, controller software limitations, nonlinearities and coupling of modes through damping. Analytical results are presented which include compensator designs for varying compensator order.

Ham, F. M.↗

Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems

Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics given our current understanding. Many plasma problems of interest fall into these categories as there are a wide range of models that exist, however each model is only useful in a certain regime and often limited by computational complexity. To ensure data-driven methods align with theory, they must be consistent and predictable when acting on data whose governing dynamics are known. Weak Sparse Identification of Nonlinear Dynamics (WSINDy) is a recently developed data-driven method that has shown promise in learning governing dynamics from data with high noise levels [1]. This work examines how WSINDy acts on ideal MHD test problems as the initial conditions are varied and specifies limiting requirements for successful equation identification. Furthermore, it is hard to recover the governing dynamics from data that emphasize a single dominant behavior. In these low information cases, Shannon information entropy is able to pick up on the redundancies in the data that affect recoverability.

97 MATHEMATICS AND COMPUTING↗

Nonlinear and adaptive estimation in reentry.

The problem of real-time estimation of a lifting reentry vehicle trajectory of the shuttle orbiter type is considered. Simulations feature large position and velocity uncertainties at radar acquisition and realistic model errors in lift, drag and other model parameters. Radar tracking and accelerometer data are simulated. Significant nonlinearities are found to exist on spacecraft acquisition. An iterated nonlinear filter is shown to perform optimally during the radar acquisition phase. An adaptive filter is shown to track time-varying model errors, such as errors in the lift and drag coefficients, down to the noise level. Such real-time model tracking (identification) is frequently required for guidance and control implementation.

Jazwinski, A. H.↗

Identification of quasi-steady compressor characteristics from transient data

The principal goal was to demonstrate that nonlinear compressor map parameters, which govern an in-stall response, can be identified from test data using parameter identification techniques. The tasks included developing and then applying an identification procedure to data generated by NASA LeRC on a hybrid computer. Two levels of model detail were employed. First was a lumped compressor rig model; second was a simplified turbofan model. The main outputs are the tools and procedures generated to accomplish the identification.

Nunes, K. B.↗

System identification of the Large-Angle Magnetic Suspension Test Fixture (LAMSTF)

The Large-Angle Magnetic Suspension Test Fixture (LAMSTF), a laboratory-scale research project to demonstrate the magnetic suspension of objects over wide ranges of attitudes, has been developed. This system represents a scaled model of a planned Large-Gap Magnetic Suspension System (LGMSS). The LAMSTF consists of a small cylindrical permanent magnet suspended element which is levitated above a planar array of five electromagnets mounted in a circular configuration. The cylinder is a rigid body and can be controlled to move in five independent degrees of freedom. Six position variables are sensed indirectly by using infrared light-emitting diodes and light-receiving phototransistors. The motion of the suspended cylinder is in general nonlinear and hence only the linear, time-invariant perturbed motion about an equilibrium state is considered. One of the main challenges in this project is the control of the suspended element over a wide range of orientations. An accurate dynamic model plays an essential role in controller design. The analytical model is first derived and open-loop characteristics discussed. The system is shown to be highly unstable and requires feedback control for system identification. Projection filters are first proposed to identify the state space model from closed-loop input/output test data in the time domain. This method is then extended to identify linear systems from the frequency test data. A canonical transformation matrix is also derived to transform the identified state space model into the physical coordinate. The LAMSTF system is stabilized by using a linear quadratic regulator (LQR) feedback controller for closed-loop identification. The rate information is obtained by calculating the back difference of the sensed position signals. Only the closed-loop random input/output data are recorded. Preliminary results from numerical simulations demonstrate that the identified system model is fairly accurate from either time domain or frequency-domain data. Experiments will be performed to validate the proposed closed-loop identification algorithms.

Huang, Jen-Kuang↗

Sliding-Mode Control Applied for Robust Control of a Highly Unstable Aircraft

An investigation into the application of an observer based sliding mode controller for robust control of a highly unstable aircraft and methods of compensating for actuator dynamics is performed. After a brief overview of some reconfigurable controllers, sliding mode control (SMC) is selected because of its invariance properties and lack of need for parameter identification. SMC is reviewed and issues with parasitic dynamics, which cause system instability, are addressed. Utilizing sliding manifold boundary layers, the nonlinear control is converted to a linear control and sliding manifold design is performed in the frequency domain. An additional feedback form of model reference hedging is employed which is similar to a prefilter and has large benefits to system performance. The effects of inclusion of actuator dynamics into the designed plant is heavily investigated. Multiple Simulink models of the full longitudinal dynamics and wing deflection modes of the forward swept aero elastic vehicle (FSAV) are constructed. Additionally a linear state space models to analyze effects from various system parameters. The FSAV has a pole at +7 rad/sec and is non-minimum phase. The use of 'model actuators' in the feedback path, and varying there design, is heavily investigated for the resulting effects on plant robustness and tolerance to actuator failure. The use of redundant actuators is also explored and improved robustness is shown. All models are simulated with severe failure and excellent tracking, and task dependent handling qualities, and low pilot induced oscillation tendency is shown.

Vetter, Travis Kenneth↗

Estimation of Aircraft Nonlinear Unsteady Parameters From Wind Tunnel Data

Aerodynamic equations were formulated for an aircraft in one-degree-of-freedom large amplitude motion about each of its body axes. The model formulation based on indicial functions separated the resulting aerodynamic forces and moments into static terms, purely rotary terms and unsteady terms. Model identification from experimental data combined stepwise regression and maximum likelihood estimation in a two-stage optimization algorithm that can identify the unsteady term and rotary term if necessary. The identification scheme was applied to oscillatory data in two examples. The model identified from experimental data fit the data well, however, some parameters were estimated with limited accuracy. The resulting model was a good predictor for oscillatory and ramp input data.

Klein, Vladislav↗

Optimized System Identification

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Juang, Jer-Nan↗

Hybrid Wing Body Model Identification Using Forced-Oscillation Water Tunnel Data

Static and dynamic testing of the NASA 0.7 percent scale Hybrid Wing Body (HWB) configuration was conducted in the Rolling Hills Research Corporation water tunnel to investigate aerodynamic behavior over a large range of angle-of-attack and to develop models that can predict aircraft response in nonlinear unsteady flight regimes. This paper reports primarily on the longitudinal axis results. Flow visualization tests were also performed. These tests provide additional static data and new dynamic data that complement tests conducted at NASA Langley 14- by 22-Foot Subsonic Tunnel. HWB was developed to support the NASA Environmentally Responsible Aviation Project goals of lower noise, emissions, and fuel burn. This study also supports the NASA Aviation Safety Program efforts to model and control advanced transport configurations in loss-of-control conditions.

Murphy, Patrick C.↗

Practical Aspects of Multiple-Input Design for Aircraft System Identification Flight Tests

Practical aspects of multiple-input design methods for aircraft system identification flight tests are discussed. The orthogonal optimized multisine multiple-input design technique is explained and demonstrated, along with useful variations. Practical implementation and application issues associated with applying orthogonal optimized multisine inputs in flight are explained, and solutions are demonstrated using flight data from full-scale and subscale aircraft, as well as simulated flight data from an F-16 nonlinear simulation. Topics include truncated and extended excitation inputs, variations for control effectors with limited movement capabilities, aircraft dynamic response to excitation inputs, pilot implementation, statistical uncertainty quantification, multiple-input efficiency and effectiveness, flight testing with active feedback control, frequency-response estimation, control actuator modeling, and control interaction effects. Examples demonstrate that the orthogonal optimized multisine input design method is a practical, versatile, and effective approach for designing multiple excitation inputs for aircraft system identification flight tests.

Multiple-Input Design↗

Stabilization of solitons under competing nonlinearities by external potentials

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗

Parametric Identification of Nonlinear Dynamical Systems

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Feeny, Brian↗

Nonlinear spectral analysis of ion acoustic solitons arising from a streaming charged object using the numerical inverse scattering transform

Observations of nonlinear coherent plasma phenomena in spacecraft and terrestrial experiments often rely on visual identification of solitary modes because nonlinear coherent modes are broadband in a Fourier transform based analysis. We implement an alternative spectral decomposition known as the inverse scattering transform and demonstrate its ability to successfully isolate nonlinear modes on the homogeneous and forced Korteweg–De Vries equation which models these nonlinear modes. We also demonstrate for the first time that this decomposition is useful when forcing is applied. This is because the stable modes generated by localized forcing are similar to the homogeneous solutions where the inverse scattering transform is a rigorous decomposition. This spectral technique is then applied to simulations of ion acoustic waves generated by a 10 mm spherical debris object interacting with the ionospheric plasma orbiting at 2000 km altitude. The algorithm is found to successfully detect the resultant solitons. This demonstrates the feasibility of using this spectral technique as a real time analysis tool for screening spacecraft data for nonlinear solitary modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generation of a Reduced-Order Model of an Unmanned Combat Air Vehicle Using Indicial Response Functions

Within the NATO STO AVT-251 Task Group, a generic Unmanned Combat Air Vehicle (UCAV) planform was redesigned based on requirements derived from parts of the flight envelope of the defined mission. Because of the lambda-shape planform and associated flow phenomena including shocks and vortices, the aerodynamic design process relies heavily on high-fidelity predictions from computational fluid dynamics (CFD). These simulations enable accurate flight dynamics predictions, allowing for the identification of any potential performance issues early in the design process. Potentially, a complete flight dynamics model can be derived from CFD calculations provided that the underlying reduced order model (ROM) captures the underlying physics contained within the CFD results. This work investigates the creation of a nonlinear ROM using indicial response functions. The response functions are obtained using a grid motion approach that separates the effects of angle of attack and pitch rate. This approach is demonstrated using three different CFD codes from various organizations: ENSOLV at Royal Netherlands Aerospace Centre, USM3D at NASA Langley Research Center, and Kestrel at the United States Air Force Academy. ROM predictions were generated for a manoeuver resembling a low-speed pull-up. The predictions are found to be sensitive to the quality of the steady-state solutions from which step-response calculations were started, as well as the convergence of the step responses themselves. Nevertheless, the indicial response method is shown to provide aerodynamic predictions with acceptable accuracy including transient effects, and as such is a promising method for computationally efficient flight dynamics predictions.

Michel P.C. van Rooij↗

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) for matching single-input single-output (SISO) transfer function models to empirical frequency response data is described. The program was written in MATLAB and has a graphical user interface (GUI). It is interactive in that the user manually builds the transfer function model using ``elementary factors'' (gain, delay, differentiators and integrators, and first- and second-order poles and zeros) and adjusts their values with sliders or entry fields. A nonlinear optimization can also be used to determine maximum-likelihood estimates of the transfer function parameters and their associated uncertainties. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and other system identification problems. FRFit is demonstrated using example problems, including the identification of aircraft transfer functions and rational function approximations of Theodorsen's function.

Frequency response↗